Information on Result #815128
Linear OOA(3167, 3292, F3, 2, 31) (dual of [(3292, 2), 6417, 32]-NRT-code), using OOA 2-folding based on linear OA(3167, 6584, F3, 31) (dual of [6584, 6417, 32]-code), using
- construction X applied to C([0,15]) ⊂ C([0,13]) [i] based on
- linear OA(3161, 6562, F3, 31) (dual of [6562, 6401, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(3145, 6562, F3, 27) (dual of [6562, 6417, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(36, 22, F3, 3) (dual of [22, 16, 4]-code or 22-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3167, 3292, F3, 3, 31) (dual of [(3292, 3), 9709, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3167, 3292, F3, 4, 31) (dual of [(3292, 4), 13001, 32]-NRT-code) | [i] | ||
| 3 | Linear OOA(3167, 3292, F3, 5, 31) (dual of [(3292, 5), 16293, 32]-NRT-code) | [i] | ||
| 4 | Digital (136, 167, 3292)-net over F3 | [i] | ||